Multiparticle Quantum Scattering in Constant Magnetic Fields

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Christian Gérard; Izabella Łaba

This monograph offers a rigorous mathematical treatment of the scattering
theory of quantum N-particle systems in an external constant magnetic field. In
particular, it addresses the question of asymptotic completeness, a
classification of all possible trajectories of such systems according to their
asymptotic behavior. The book adopts the so-called time-dependent approach to
scattering theory, which relies on a direct study of the Schrödinger
unitary group for large times. The modern methods of spectral and scattering
theory introduced in the 1980s and 1990s, including the Mourre theory of
positive commutators, propagation estimates, and geometrical techniques, are
presented and heavily used. Additionally, new methods were developed by the
authors in order to deal with the (much less understood) phenomena due to the
presence of the magnetic field.

The book is a good starting point for graduate students and researchers in
mathematical physics who wish to move into this area of research. It includes
expository material, research work previously available only in the form of
journal articles, as well as some new unpublished results. The treatment of the
subject is comprehensive and largely self-contained, and the text is carefully
written with attention to detail.

This monograph offers a rigorous mathematical treatment of the scattering
theory of quantum N-particle systems in an external constant magnetic field. In
particular, it addresses the question of asymptotic completeness, a
classification of all possible trajectories of such systems according to their
asymptotic behavior. The book adopts the so-called time-dependent approach to
scattering theory, which relies on a direct study of the Schrödinger
unitary group for large times. The modern methods of spectral and scattering
theory introduced in the 1980s and 1990s, including the Mourre theory of
positive commutators, propagation estimates, and geometrical techniques, are
presented and heavily used. Additionally, new methods were developed by the
authors in order to deal with the (much less understood) phenomena due to the
presence of the magnetic field.

The book is a good starting point for graduate students and researchers in
mathematical physics who wish to move into this area of research. It includes
expository material, research work previously available only in the form of
journal articles, as well as some new unpublished results. The treatment of the
subject is comprehensive and largely self-contained, and the text is carefully
written with attention to detail.

Graduate students and research mathematicians interested in
mathematical physics and differential equations.

Reviews:

The book is well organized and well written … the authors have
successfully achieved their stated aim of writing a book which is of interest
both to a wider section of the mathematical physics community … and to
graduate students and researchers in the field of spectral and scattering
theory for magnetic Schrödinger operators.

Contents

Preface

Notation

Chapter 1. Fundamentals

Index

Readership

Graduate students and research mathematicians interested in
mathematical physics and differential equations.

Reviews

The book is well organized and well written … the authors have
successfully achieved their stated aim of writing a book which is of interest
both to a wider section of the mathematical physics community … and to
graduate students and researchers in the field of spectral and scattering
theory for magnetic Schrödinger operators.